Finishing off our discussion of multi-objective optimization in evolutionary algorithms, we review Pareto ranking approaches and how they differ in selective pressure and how to use "fitness scaling" to tune that selective pressure. Selective pressure must be controlled in multi-objective genetic algorithms (MOGA's) to prevent significant loss of diversity while the set of candidate solutions moves toward the frontier. We then revisit fitness sharing and clearing approaches that help increase diversity (not just maintain it) along the frontier.
This gives us an opportunity to pivot back to the one-objective case to discuss possible enhancements based on lessons learned in the multi-objective case. We start by discussing parallel GA (PGA) in contrast with distributed GA (DGA). In the latter case, the population is split among multiple "demes" that have infrequent (but guaranteed) migration among them. We discuss how metapopulation effects increase the role of drift in each subpopulation, which leads to a new source of novel variation (aside from mutation). This effect is closely tied to the "shifting-balance theory" of Sewall Wright (from population genetics). This strength allows DGA to out-perform (in terms of finding global optima) simpler GA architectures (even PGA).
We then turn back to single-objective optimization on a single processor and introduce multi-modal optimization -- where the goal is to find all local optima (including the global optima) instead of only the global optima. This is a sort of "peak finder" for optimization objectives. A good multi-modal optimizer will need to maintain diversity using mechanisms similar to those used in multi-objective optimization, where now each "niche" will correspond to a different local peak as opposed to a different tradeoff among multiple objectives. We will go into multi-modal optimization techniques in the next lecture.
Whiteboard notes for this lecture can be found at: https://www.dropbox.com/s/xuij7chgk4axqoe/IEE598-Lecture4A-2022-02-10-From_Multiobj_Genetic_Algorithms_to_DGA_PGA_and_Multimodal_Opt.pdf?dl=0
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